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| ACKNOWLEDGMENTS CHAPTER 1. INTRODUCTION 1.1. Some Physical Examples of Systems of Conservation Laws 1.2. The Importance Of DiSSipative Mechanisms 1.3. The Common Structure of the Physical Systems Of Conservation Laws and Friedrichs’Theory Of SymmetriC Systems 1.4.Linear and Nonlinear Wave Propagation and the Theory Of Nonlinear Simple Waves 1.5. WeaklY Nonlinemr AsymptotiCS—Nonlinear GeometriC OptiCS 1.6. A Rigorous Justification Of Weakly Nonlinear AsymptOtiCS in a Special Case 1.7. Some Additional Applications Of Weakly Nonlinear Asymptotics in the Modeling of Complex Systems Bibliography for Chapter 1 CHAPTER 2. SMOOTH SOLUTIONS AND THE EQUATIONS OF INCOMPRESSIBLE FLUID FLOW 2.1.The Local ExiStence Of Smooth Solutions for Systems 0f Conservation Laws 2.2. A COntinuatiOn Principle for Smooth Solutions 2.3. Uniformly Local Sob01ev Spaces 2.4. CompreSSible and IncompreSSible Fluid F10W 2.S. Equations for Low Mach Number Combustion BibliOgraphy for Chapter 2 CEAPTER 3.THE FORMATION OF SHOCK WAVES IN SMOOTH SOLUTIONS 3.1. Shock Formation for Scalar Laws in Several Space Variables 3.2. Shock Formation in Plane Wave Solutions Of General mom Systems 3.3.Detailed Results on Shock Formation for 2×2 Systems 3.4. Breakdown for a QuaSi—Linear Wave Equation in 3一D 3.5. Some Open Problems Involying Shock Formation in Smooth S01utions BibliOgraphy for Chapter 3 CHAPTER 4.THE EXISTENCE AND STABILITY OF SHOCK FRONTS IN SEVERAL SPACE VARIABLES 4.1. Nonlinear Discontinuous Progressing Waves in Several Variables—Shock Front Initial Data 4.2. Some Theorems Guaranteeing the Existence of Shock FrontS CHAPTER 4.(cont.) 4.3. Lineari zation of Shock Fronts 4.4. An Introduction to Hyperbolic Mixed Problems 4.5. Quantitative Estimates for Linearized Shoc…k FrontS 4.6. Some open Problems in Multi—D Shock Wave Theory Bibliography for Chapter 4 INDEX |
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